Maximum Likelihood Estimation Algorithm Research Articles

Early Warning Analysis of Oil-Gas Field Equipment Failure Based on Statistical Model of Failure Rate

This paper proposed a method used to estimate mechanical equipment failure for oil-gas field enterprises. First, this method established a mixed failure distribution model of mechanical equipment modules. According to the collected statistical data of module defect, this method then applied MLE (Maximum Likelihood Estimation) algorithm and EM algorithm to calculate the mixed failure distribution parameters of mechanical equipment modules, so as to form the mixed distribution function of failure rate. The feasibility of this method was verified through examples. At last, the concept of risk early warning management for mechanical equipment failure was proposed based on the estimated distribution function of mechanical equipment failure rate. As a result, there are scientific grounds for the equipment maintenance & repair cycle regulated by grass-roots staff and the equipment replacement & scrapping strategy set by management-level users.

Segmentation and classification models validation area mapping of peat lands as initial value of Fuzzy Kohonen Clustering Network

Ogan Komering Ilir (OKI) is located at the eastern of South Sumatra Province, 2030′-4015′ latitude and 104020′-106000′ longitude. Digital image of land was captured from Landsat 8 satellite path 124/row 062. Landsat 8 is new generation satellite which has two sensors, Operation Land Manager (OLI) and Thermal Infra-Red Sensor (TIRS). In pre-processing step, there are a geometric correction, radiometric correction, and cropping of the digital images which resulting coordinated geography. Classification uses maximum likelihood estimator algorithm. In segmentation process and classification, grey value spread is into evenly after applying histogram technique. The results of entropy value are7.42 which is the highest of result image classification, then the smallest entropy value in the result of correction mapping are 6.39. The three of them prove that they have enough high entropy value. Then the result of peatlands classification is given overall accuracy value = = 94.0012% and overall kappa value = 0.9230 so the result of classification can be considered to be right.

Maximum likelihood estimation method for dual-rate Hammerstein systems

For a dual-rate sampled Hammerstein controlled autoregressive moving average (CARMA) system, this paper uses the polynomial transformation technology to obtain its dual-rate bilinear identification model which is suitable for the available dual-rate sampled-data, uses the maximum likelihood principle to construct a unified parameter vector of all parameters and an information vector formed by the derivative of the noise variable to the unified parameter vector, and directly identifies the parameters of the linear block and the nonlinear block for the dual-rate Hammerstein CARMA system. The unified parameter vector contains the minimum number of the unknown parameters, and the proposed maximum likelihood estimation algorithm has higher computational efficiency than the over-parameterization model based least squares algorithm.

Scale mixtures of skew-normal-Cauchy distributions

We propose the scale mixtures of multivariate skew-normal-Cauchy distributions as a new class of asymmetric heavy-tailed distributions. We derive an EM algorithm for maximum likelihood estimation.

A Variational Maximization-Maximization Algorithm for Generalized Linear Mixed Models with Crossed Random Effects.

We present a variational maximization-maximization algorithm for approximate maximum likelihood estimation of generalized linear mixed models with crossed random effects (e.g., item response models with random items, random raters, or random occasion-specific effects). The method is based on a factorized variational approximation of the latent variable distribution given observed variables, which creates a lower bound of the log marginal likelihood. The lower bound is maximized with respect to the factorized distributions as well as model parameters. With the proposed algorithm, a high-dimensional intractable integration is translated into a two-dimensional integration problem. We incorporate an adaptive Gauss-Hermite quadrature method in conjunction with the variational method in order to increase computational efficiency. Numerical studies show that under the small sample size conditions that are considered the proposed algorithm outperforms the Laplace approximation.

Maximum likelihood estimation and EM algorithm of Copas-like selection model for publication bias correction.

Publication bias occurs when the published research results are systematically unrepresentative of the population of studies that have been conducted, and is a potential threat to meaningful meta-analysis. The Copas selection model provides a flexible framework for correcting estimates and offers considerable insight into the publication bias. However, maximizing the observed likelihood under the Copas selection model is challenging because the observed data contain very little information on the latent variable. In this article, we study a Copas-like selection model and propose an expectation-maximization (EM) algorithm for estimation based on the full likelihood. Empirical simulation studies show that the EM algorithm and its associated inferential procedure performs well and avoids the non-convergence problem when maximizing the observed likelihood.

Mitigating Multipath Bias Using a Dual-Polarization Antenna: Theoretical Performance, Algorithm Design, and Simulation.

It is well known that multipath effect remains a dominant error source that affects the positioning accuracy of Global Navigation Satellite System (GNSS) receivers. Significant efforts have been made by researchers and receiver manufacturers to mitigate multipath error in the past decades. Recently, a multipath mitigation technique using dual-polarization antennas has become a research hotspot for it provides another degree of freedom to distinguish the line-of-sight (LOS) signal from the LOS and multipath composite signal without extensively increasing the complexity of the receiver. Numbers of multipath mitigation techniques using dual-polarization antennas have been proposed and all of them report performance improvement over the single-polarization methods. However, due to the unpredictability of multipath, multipath mitigation techniques based on dual-polarization are not always effective while few studies discuss the condition under which the multipath mitigation using a dual-polarization antenna can outperform that using a single-polarization antenna, which is a fundamental question for dual-polarization multipath mitigation (DPMM) and the design of multipath mitigation algorithms. In this paper we analyze the characteristics of the signal received by a dual-polarization antenna and use the maximum likelihood estimation (MLE) to assess the theoretical performance of DPMM in different received signal cases. Based on the assessment we answer this fundamental question and find the dual-polarization antenna’s capability in mitigating short delay multipath—the most challenging one among all types of multipath for the majority of the multipath mitigation techniques. Considering these effective conditions, we propose a dual-polarization sequential iterative maximum likelihood estimation (DP-SIMLE) algorithm for DPMM. The simulation results verify our theory and show superior performance of the proposed DP-SIMLE algorithm over the traditional one using only an RHCP antenna.

A semi-hidden Fritchman Markov modeling of indoor CENELEC A narrowband power line noise based on signal level measurements

To achieve error-free communication on the narrowband power line communication (NB-PLC) channel, there is need for constant measurement campaign and modeling of burst errors resulting from noise, perturbation and disturbances on the channel. This work thus reports a signal level measurement and First-Order Semi-Hidden Fritchman Markov modeling of the three major NB-PLC noise types for a typical South African residential and laboratory indoor low voltage environment. Two distinguishable disturbance scenarios: mildly disturbed and heavily disturbed were considered and Baum–Welch maximum likelihood estimation (MLE) algorithm is used to obtain the most probable model parameters that statistically depict the experimentally measured noise error sequences.

Geo-Spatial Location Estimation for Internet of Things (IoT) Networks With One-Way Time-of-Arrival via Stochastic Censoring

We develop new algorithms for geo-spatial location estimation for Internet of Things (IoT) networks by utilizing a one way time of arrival (OW-TOA) approach. We first demonstrate the limitations of current OW-TOA location estimation algorithms for IoT networks when some of the anchor nodes (ANs) are outside the communication range with the source, which results in ambiguous level-sets of the likelihood function, causing inaccurate source localization. We then show that in IoT networks, in addition to using the conventional noisy ranging measurements from nodes which are in the communication range, we can make use of the audibility information (which indicates whether a node is able/unable to communicate with the target) that each node has. By leveraging on this available information, we considerably improve the localization performance, by mitigating the well known ambiguity problem which arises when a few AN are inaudible. The first algorithm we develop is the joint source location and time offset maximum likelihood estimation (MLE) and the second is the differential source location MLE. Our algorithms require no additional hardware and the novelty lies in using the available audibility information to resolve the likelihood ambiguity. Finally, we develop the Cramer–Rao bounds of the source location estimate for both algorithms. Extensive simulations show the significant benefits of our algorithms compared to the conventional MLE algorithms.

Robust quantile regression using a generalized class of skewed distributions

It is well known that the widely popular mean regression model could be inadequate if the probability distribution of the observed responses do not follow a symmetric distribution. To deal with this situation, the quantile regression turns to be a more robust alternative for accommodating outliers and the misspecification of the error distribution because it characterizes the entire conditional distribution of the outcome variable. This paper presents a likelihood‐based approach for the estimation of the regression quantiles based on a new family of skewed distributions. This family includes the skewed version of normal, Student‐t, Laplace, contaminated normal and slash distribution, all with the zero quantile property for the error term and with a convenient and novel stochastic representation that facilitates the implementation of the expectation–maximization algorithm for maximum likelihood estimation of the pth quantile regression parameters. We evaluate the performance of the proposed expectation–maximization algorithm and the asymptotic properties of the maximum likelihood estimates through empirical experiments and application to a real‐life dataset. The algorithm is implemented in the R package lqr, providing full estimation and inference for the parameters as well as simulation envelope plots useful for assessing the goodness of fit. Copyright © 2017 John Wiley & Sons, Ltd.

Estimation of Parameters of the Two-Parameter Rayleigh Distribution Based on Progressive Type-II Censoring Using Maximum Likelihood Method via the NR and the EM Algorithms

In this article, Maximum likelihood estimates for the shape and scale parameters of two-parameter Rayleigh distribution are obtained based on progressive type-II censored samples using the Newton-Raphson (NR) method and the Expectation-Maximization (EM) algorithm. A simple algorithm discussed in [2-3] is used for generating progressive type-II censored samples. Based on this censoring scheme, approximate asymptotic variances are derived and used to construct approximate confidence intervals of the parameters. The performance of these two maximum likelihood estimation algorithms is compared in terms of simulation results of root mean squared error (RMSE) and the coverage rates. Simulation results showed that in nearly all the combination of simulation conditions the estimators based on the EM algorithm have less root mean squared error (RMSE) and narrower widths of confidence intervals compared to those obtained using the NR algorithm. Finally, an illustrative example with real-life data sets is provided to illustrate how maximum likelihood estimation using the two algorithms works in practice.

Efficient moment calculations for variance components in large unbalanced crossed random effects models

Large crossed data sets, described by generalized linear mixed models, have become increasingly common and provide challenges for statistical analysis. At very large sizes it becomes desirable to have the computational costs of estimation, inference and prediction (both space and time) grow at most linearly with sample size. Both traditional maximum likelihood estimation and numerous Markov chain Monte Carlo Bayesian algorithms take superlinear time in order to obtain good parameter estimates. We propose moment based algorithms that, with at most linear cost, estimate variance components, measure the uncertainties of those estimates, and generate shrinkage based predictions for missing observations. When run on simulated normally distributed data, our algorithm performs competitively with maximum likelihood methods.

Measurement-Based Massive MIMO Channel Modeling for Outdoor LoS and NLoS Environments

In this paper, a measurement campaign for massive multiple-input multiple-output (MIMO) channel characterization in both line-of-sight (LoS) and non-LoS outdoor environments is introduced. The measurements are conducted at the center frequency of 15 GHz with a bandwidth of 4 GHz. A virtual $40\times 40$ planar antenna array formed by stepping a vertically-polarized bi-conical omni-directional antenna (ODA) along regularly-spaced grids is used in the receiver (Rx). The transmitter is equipped with a single ODA. To investigate channel variations over the Rx array, this 1600-element Rx array is split into multiple $7\times 7$ sub-arrays, and a maximum-likelihood parameter estimation algorithm implemented using the space-alternating generalized expectation-maximization principle is applied to extracting multipath components (MPCs) from sub-array outputs. The spatial variability of $K$ -factor, composite channel spreads in delay, azimuth, and elevation of arrival are investigated. Based on the estimated MPCs’ parameters, multipath clusters are identified and associated across the array to find the so-called spatial-stationary (SS) clusters. From several hundreds of SS-clusters extracted, we establish a stochastic model for their life distances in horizontal and vertical directions, two-dimensional (2-D) life region, and variations of cluster spreads. These findings are important for massive MIMO channel modeling in the cases, where 2-D large-scale arrays are considered.

Maximum Likelihood Time Delay Estimation Based on Monte Carlo Importance Sampling in Multipath Environment

In multipath environment, the computation complexity of single snapshot maximum likelihood for time delay estimation is huge. In particular, the computational complexity of grid search method increases exponentially with the increase of dimension. For this reason, this paper presents a maximum likelihood estimation algorithm based on Monte Carlo importance sampling technique. Firstly, the algorithm takes advantage of the channel frequency response in order to build the likelihood function of time delay in multipath environment. The pseudoprobability density function is constructed by using exponential likelihood function. Then, it is crucial to choose the importance function. According to the characteristic of the Vandermonde matrix in likelihood function, the product of the conjugate transpose Vandermonde matrix and itself is approximated by the product of a constant and an identity matrix. The pseudoprobability density function can be decomposed into product of many probability density functions of single path time delay. The importance function is constructed. Finally, according to probability density function of multipath time delay decomposed by importance function, the time delay of the multipath is sampled by Monte Carlo method. The time delay is estimated via calculating weighted mean of sample. Simulation results show that the performance of proposed algorithm approaches the Cramér-Rao bound with reduced complexity.

Photon-by-Photon Hidden Markov Model Analysis for Microsecond Single-Molecule FRET Kinetics.

The function of biological macromolecules involves large-scale conformational dynamics spanning multiple time scales, from microseconds to seconds. Such conformational motions, which may involve whole domains or subunits of a protein, play a key role in allosteric regulation. There is an urgent need for experimental methods to probe the fastest of these motions. Single-molecule fluorescence experiments can in principle be used for observing such dynamics, but there is a lack of analysis methods that can extract the maximum amount of information from the data, down to the microsecond time scale. To address this issue, we introduce H2MM, a maximum likelihood estimation algorithm for photon-by-photon analysis of single-molecule fluorescence resonance energy transfer (FRET) experiments. H2MM is based on analytical estimators for model parameters, derived using the Baum-Welch algorithm. An efficient and effective method for the calculation of these estimators is introduced. H2MM is shown to accurately retrieve the reaction times from ∼1 s to ∼10 μs and even faster when applied to simulations of freely diffusing molecules. We further apply this algorithm to single-molecule FRET data collected from Holliday junction molecules and show that at low magnesium concentrations their kinetics are as fast as ∼104 s-1. The new algorithm is particularly suitable for experiments on freely diffusing individual molecules and is readily incorporated into existing analysis packages. It paves the way for the broad application of single-molecule fluorescence to study ultrafast functional dynamics of biomolecules.

Asymptotic properties and expectation-maximization algorithm for maximum likelihood estimates of the parameters from Weibull-Logarithmic model

In this article, we consider a lifetime distribution, the Weibull-Logarithmic distribution introduced by [6]. We investigate some new statistical characterizations and properties. We develop the maximum likelihood inference using EM algorithm. Asymptotic properties of the MLEs are obtained and extensive simulations are conducted to assess the performance of parameter estimation. A numerical example is used to illustrate the application.

Segmentation and Classification Models Validation Area Mapping of Peat Lands as Initial Value of Fuzzy Kohonen Clustering Network

Ogan Komering Ilir (OKI) is located at the eastern of South Sumatra Province, 2 0 30'-4 0 15' latitude and 104 0 20'-106 0 00' longitude. Digital image of land was captured from Landsat 8 satellite path 124/row 062. Landsat 8 is new generation satellite which has two sensors, Operation Land Manager (OLI) and Thermal Infra-Red Sensor (TIRS). In pre-processing step, there are a geometric correction, radiometric correction, and cropping of the digital images which resulting coordinated geography. Classification uses maximum likelihood estimator algorithm. In segmentation process and classification, grey value spread is into evenly after applying histogram technique. The results of entropy value are7.42 which is the highest of result image classification, then the smallest entropy value in the result of correction mapping are 6.39. The three of them prove that they have enough high entropy value. Then the result of peatlands classification is given overall accuracy value = = 94.0012% and overall kappa value = 0.9230 so the result of classification can be considered to be right.

Sparsity‐aware multitarget localisation for distributed MIMO radar against phase synchronisation mismatch

The authors address the problem of coherent multitarget localisation for distributed multiple-input multiple-output (MIMO) radar, in the presence of phase synchronisation mismatch between each transmitter-receiver pair. The inherent sparsity of targets in the surveillance area can be exploited to represent radar data and then target locations are accurately estimated using sparse reconstruction. However, due to the difficulty of perfect phase synchronisation, the localisation technique is usually required to eliminate the phase errors. This study jointly considers the phase error correction problem in the context of multitarget localisation. In this novel method, the direct position determination of multitarget is obtained by estimating the spare reflection coefficients and phase errors alternately. Numerical simulation results demonstrate that the authors’ iterative block sparse Bayesian learning via maximum likelihood estimation algorithm obtains enhanced estimation accuracy against the phase synchronisation mismatch.

Node localization algorithm of wireless sensor networks with mobile beacon node

When maximum movement distance of beacon node is limited, in order to improve the localization accuracy of sensor nodes, node localization algorithm of wireless sensor networks with mobile beacon node (NLA_MB) is proposed. NLA_MB algorithm divides the movement area of beacon node into some hexagonal grids, and establishes optimization model of node localization errors according to the movement path constraint, movement distance constraint and other constraints of beacon node. Beacon node uses heuristic method to solve the model approximately based on virtual force theory and location information of guide sensor nodes, and obtains a moving path which is suitable for the current node distribution. According to location information of beacon node or anchor sensor nodes, sensor nodes use maximum likelihood estimation algorithm to calculate their own location coordinates. Simulation results show that NLA_MB algorithm is suitable for the distribution scenarios of sensor nodes, such as full coverage distribution, L-type distribution, Tian-type distribution and U-type distribution. It can increase the number of sojourn locations of beacon node and average number of anchor points of sensor nodes, and reduce average localization error of sensor nodes. Under certain conditions, NLA_MB algorithm outperforms DOUBLE_SCAN, ZSCAN, MLE, RSCAN and DBMS algorithms.

Nonlinear regression models under skew scale mixtures of normal distributions

Normal nonlinear regression models are applied in some areas of the sciences and engineering to explain or describe the phenomena under study. However, it is well known that several phenomena are not always represented by the normal model due to lack of symmetry or the presence of heavy- and light-tailed distributions related to the normal law in the data. This paper proposes an extension of nonlinear regression models using the skew-scale mixtures of normal (SSMN) distributions proposed by Ferreira et al. (2011). This class of models provides a useful generalization of the symmetrical nonlinear regression models since the random term distributions cover both asymmetric and heavy-tailed distributions, such as the skew-t-normal, skew-slash and skew-contaminated normal, among others. An expectation–maximization (EM) algorithm for maximum likelihood (ML) estimates is presented and the observed information matrix is derived analytically. Some simulation studies are presented to examine the performance of the proposed methods, with relation to robustness and asymptotic properties of the ML estimates. Finally, an illustration of the method is presented considering a dataset previously analyzed under normal and skew-normal (SN) nonlinear regression models. The main conclusion is that the ML estimates from the heavy tails SSMN nonlinear models are more robust against outlying observations compared to the corresponding SN estimates.